Question

The results given in the below table were obtained during kinetic studies of the following reaction: 2A + B → C + D

X and Y in the given table are respectively :

• A. 0.4, 0.4
• B. 0.3, 0.4
• C. 0.4, 0.3
• D. 0.3, 0.3

Answer 1

The correct option is B

0.3, 0.4

Explanation for the correct answer:-

option (B) 0.3, 0.4

Step 1: Writing experiments I, II, and III

According to the question, the rate law of the 3 experiments is:

$\mathrm{rate}=\mathrm{k}{\left[\mathrm{A}\right]}_0^{\mathrm{p}}{\left[\mathrm{B}\right]}_0^{\mathrm{q}}$

Experiment (I): $6\times {10}^{–3}=\mathrm{K}{(0.1)}^{\mathrm{p}}{(0.1)}^{\mathrm{q}}$

Experiment (II): $2.40\times {10}^{–2}=\mathrm{K}{(0.1)}^{\mathrm{p}}{(0.2)}^{\mathrm{q}}$

Experiment (III): $1.20\times {10}^{–2}=\mathrm{K}{(0.2)}^{\mathrm{p}}{(0.1)}^{\mathrm{q}}$

Step 2: Finding the values of p and q

Dividing experiment (I) with (II) we get,

$$\begin{gathered} \frac{1}{4}={\left(\frac{1}{2}\right)}^q \\ \Rightarrow {\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^q \\ \Rightarrow \mathrm{q}=2 \end{gathered}$$

Dividing experiment (I) with (III) we get,

$$\begin{gathered} \frac{1}{2}={\left(\frac{1}{2}\right)}^q \\ \Rightarrow \frac{1}{2}={\left(\frac{1}{2}\right)}^q \\ \Rightarrow \mathrm{p}=1 \end{gathered}$$

Step 3: Finding the values of x and y

Dividing experiment (I) with experiment (IV) we get,

$$\begin{gathered} \left(\frac{6.00\times {10}^{-3}}{7.20\times {10}^{-2}}\right)={\left(\frac{0.1}{x}\right)}^1\times {\left(\frac{0.1}{0.2}\right)}^2 \\ \Rightarrow \frac{1}{12}=\left(\frac{0.1}{x}\right)-\left(\frac{1}{4}\right) \\ \Rightarrow \left[\mathrm{x}\right]=0.3 \end{gathered}$$

Dividing experiment (I) with experiment (V) we get,

$$\begin{gathered} \left(\frac{6.00\times {10}^{-3}}{2.88\times {10}^{-1}}\right)={\left(\frac{0.1}{0.3}\right)}^1\times {\left(\frac{0.1}{7}\right)}^2 \\ \Rightarrow \frac{1}{48}=\left(\frac{1}{3}\right)\times \left(\frac{{10}^{-2}}{y^2}\right) \\ \Rightarrow y^2=0.16 \\ \Rightarrow y=0.4 \end{gathered}$$

Hence it is the correct option

Therefore, option (B) 0.3, 0.4 is the correct answer.